歷史演講 PAST TALKS

詳如附件

Abstract： In this talk we will review some global existence and decay to equilibrium result for some crystal surface and thin film models. In particular, we will prove that, under certain (explicit) size restriction in a critical (with regards to the scaling of the equation) spaces, the PDE admits a global solution and, furthermore, this solution decays to equilibrium.

Abstract： In this talk, we establish the existence of a solution to the 3-dimensional Navier-Stokes equations interacting with elastic shell on a moving domain. First, I will introduce the ALE formulation which transform our moving domain into a fixed domain. The method is very useful for the free boundary problem. Second, I will explain how the solution is constructed in an optimal sobolev space and explain the difficulties of our study. Finally, we can compare two kinds of well-posedness problems of Navier-Stokes equations: interacting with elastic shell and with the surface tension.

Abstract： We first review uniqueness theorems for phase retrieval with a coded diffraction pattern and discuss how non-uniqueness ruins phase retrieval with a plain diffraction pattern. We then present recent progress in uniqueness issues for ptychography and blind ptychography, which does not assume the knowledge of the mask.

Abstract： Computational topology is a relatively young field in algebraic topology. Tools from computational topology have proven successful in many scientific disciplines, such as fluid dynamics, biology, material science, climatology, etc. In this talk, we will give a brief introduction to computational topology, focusing primarily on persistent homology. Applications to various datasets from cell biology and climatology will be presented to illustrate the methods.

*須自備筆電且安裝好tensorflow與keras

Abstract: I will introduce some new results on the multiple solutions of a singular nonlinear boundary value problem, which arises in a study of the laminar flow in a porous pipe with an expanding or contracting wall. For the singular nonlinear BVP, the correct boundary conditions are derived to guarantee that its linearization has a unique smooth solution. Then a numerical technique is proposed to find all possible multiple solutions. The numerical technique designed is reliable, and may be further applied to solve a variety of nonlinear equations that arise from other flow problems.

Abstract： We consider the structure of singular solutions for elliptic equations with the Hardy potential and critical nonlinearity under quite general conditions on the potential terms. It is shown that there exists a unique special singular solution, and other infinitely many singular solutions are oscillatory around the special singular solution. We also study the asymptotic behavior of the solutions around the singular point. Our results can be applied to various problems such as the scalar feld equation, a self-replication model and the Cafarelli-Kohn-Nirenberg inequality.

Abstract： Weak noise input can play a constructive role in leading to synchronization of interacting oscillators commonly studied in applied sciences. Under proper conditions, this phenomenon may also be observed in noninteracting oscillators. In this study, we provide explanations in network synchrony under different classes of oscillators.

Abstract: I will introduce some new results on the asymptotic solutions of a nonlinear boundary value problem, which arises in a study of laminar flow in a uniformly porous channel with retractable walls and an applied transverse magnetic field. For different ranges of the control parameters arising in the BVP, four cases are considered using different singular perturbation methods. Numerical solutions presented for each case agree well with asymptotic solutions, which illustrates that the asymptotic solutions constructed are more reliable. Finally, the influences of some parameters on flow field are discussed to develop a better understanding of the flow problem.

Abstract: We study a logistic model-based active learning procedure for binary classification problems, in which we adopt a batch subject selection strategy with a modified sequential experimental design method. Meanwhile, accompanying the proposed subject selection scheme, we conduct a greedy variable selection procedure such that we can update the classification model with all labeled training subjects efficiently. The proposed algorithm repeatedly performs both subject and variable selection steps until a prefixed stopping criterion is reached. Our numerical results show that the proposed procedure has competitive performances, with smaller training size and a more compact model compared with that of the classifier trained with all variables and a full data set. We also apply the proposed procedure to two data sets, wave and MAGIC gamma telescope data, to confirm the performance of our method. (This is a joint work with Professor Yuan-Chin Chang and Professor Ray-Bing Chen.)

*須自備筆電且安裝好tensorflow與keras

Abstract： In this talk, we establish general theorem and boundary value theorem for \beta harmonic functions. This is a by-product in the study of Navier-Stokes equations and harmonic functions.

摘要： 三位自中央數學系出來的傑出校友談談自己從大學到研究所的心路歷程。

Abstract: Existence and uniqueness of solutions to the martingale problem posed by stochastic Navier-Stokes equations will be established. This entails Galerkin approximations, tightness, convergence of martingale problems, and identification of the limit. Pathwise uniqueness of the limit will also be shown.

Abstract: The concept of a martingale problem due to Stroock and Varadhan will be introduced in finite and infinite dimensions. After discussing the functional analytic setup of stochastic Navier-Stokes equations (SNSEs), the martingale problem posed by SNSEs will be studied.

*須自備筆電且安裝好tensorflow與keras

*須自備筆電且安裝好tensorflow與keras

Abstract： 自從Dr. Drew Conway用Venn Diagram的三個圈圈來描述資料科學家應該具備的技能和知識，在近來討論“資料科學”的演講或科普文章中，常常可以發現許多作者們用越來越複雜的圈圈來表達他們對資料科學的“定義”；很顯然大家尚未有定論所以才會如此。這些討論大半是從應用和技術層面來探討資料科學，他們提供了一些想進入資料科學領域的人一個學習的路徑。在這個非典型的演講中，我想換一個角度思考這個問題 -- “我想 (能) 做一個資料科學家嗎？” 我將借用幾個統計方法及機器學習方法的發展過程，來跟大家分享統計學家或近代所謂的“資料科學家”是怎麼思考問題的。藉由瞭解這個領域中的工作者如何思考他們面對的問題，進而發展出解決他們面對的問題的工具 – 從計算或統計的層面來討論，希望可以幫忙你思考你的選擇。但這不是一個技術性的演講，我們將不會深入談論技術的部分。另外，由於這是一個發展中的領域，我僅僅以個人經驗來討論，將無可避免會有偏差，所以更希望大家準備好自己的問題，我們將可以利用這機會討論。

Abstract: 在本演講中，我們將探討統計與數據科學 (statistics and data science) 間的關聯與互動。一般而言，統計主要在探討我們所處隨機世界裡的必然性與隨機性:透過資料收集、整理，及分析，來了解生活中的各種狀況，其中包括以視覺化的統計圖表或動態影片，來呈現數據的變化趨勢。再利用統計模型以分析數據，並根據分析結果，對所探討的議題，給出合理的推論與詮釋。長期以來，統計著重在處理較多具結構性的數據，數據科學則偏向關注屬於非結構化的數據之分析，例如文字、聲音，及影像資料等的辨識或分類問題。 近年來，由於數據科學的蓬勃發展，產生許多非典型的數據分析議題，對統計等相關學門之研究也帶來新的挑戰。另一方面，數據科學若要更加精進及提昇應用成效，亦須進一步強化與統計等相關領域研究之連結與互動。易言之，數據科學宜整合統計、數學，及計算等領域的各種方法，從數據中擷取現有資訊，再將其轉化成各種新的數據形式，以利進一步分析並給出推論。我們將藉若干實務上可能遇到的問題，例如在生產線上，如何辨識產品是否有瑕疵；及如何根據過去的電力負載資訊，對未來的負載做預測，以說明統計思維與方法，可有效地融入數據科學之相關研究中。

*須自備筆電且安裝好tensorflow與keras

摘要： 1. 學生是良師—教學模式的改變 2. 翻轉教學 3. 萬事起頭難—公會演講、深耕服務… 4. 產學合作—研究統計諮詢 5. 跨域學習的新時代 6. 師生共學

摘要： 為何選擇出國留學？ 今年我很幸運的能錄取喬治亞理工學院(Georgia Tech)的計算科學與工程(CSE)碩士，希望這次的分享能幫助到有想出國念書或轉領域的同學。 在這次留學演講分享 (1) 經歷與經驗 (2) 出國念書的動機 (3) 如何在轉計算(CS,CSE)領域所做的準備及計算領域在北美研究所申請現況 (4) 實習中的經驗與挫敗 (5) 英文考試(TOEFL, GRE)準備 (6) 文件(Resume, Personal Statement, Letter of Recommendation)的擬稿撰寫與選校方式以及美國研究所選才方式

畢業要幹嘛? 隨著大數據、複雜的影像處理及AI廣泛應用 數學人才水漲船高 想要更了解念統計-資料科學的未來出入!? 快來卡個好位 聽聽看學姐怎麼說!!

*須自備筆電且安裝好tensorflow與keras

Abstract： A reaction-diffusion system consists of kinetic term and diffusion term.Diffusion homogenizes a solution. It looks a simple equation. However, a pattern of solution sometimes performs by combing a kinetic effect, which is called Turing’s instability. In this talk, I will explain that the reaction-diffusion systems are close to the other types of partial differential equations by using the singular perturbation method. Indeed, I will present three types of approximations: cross-diffusion systems, non-local evolutionary equations with any even kernels, semi linear wave equation by reaction-diffusion systems. In some cases, the pattern formation by cross-diffusivity or the nonlocal term can be explained by Turing’s instability through the reaction-diffusion approximation.

*須自備筆電且安裝好tensorflow與keras

Abstract： John W. Tukey 在探索式資料分析(Exploratory Data Analysis, EDA)書中開宗明義提到“It is important to understand what you CAN DO before you learn to measure how WELL you seem to have DONE it.” 學習可以做什麼，有助於在資料分析的過程中達到事半功倍的效果 。EDA的作用在於從「看」資料獲得資料所傳達的訊息，所注重的是簡單的算術與容易建構的圖、表。透過EDA對於圖表中所顯露的型樣(pattern)做一初步的認知與描述，再進一步以人類的心智(mind)對所接受的訊息做全面的分析與判斷，以探索潛藏於資料中的訊息。強調的是探索式的分析而非嚴謹的模式確認。 現代資料分析與統計應用面臨高維度與高複雜度之巨量資料 (BIG Data) 艱難挑戰，而現有之統計繪圖法與視覺化方法不足以讓使用者一窺資料之全貌，以選擇合適之分析方法與統計模型。EDA已經問世四十年了，而箱型圖(box-and-whisker plot)與散佈圖(scatterplot) 仍然是二十一世紀最主要之繪圖與視覺化工具。發展有效率之繪圖法與視覺化環境以幫助使用者在處理由先進科技與複雜實驗所產生之資料時瞭解what one CAN DO乃統計學家重要職責。 本演講將介紹相關研究團隊多年來發展之矩陣視覺化環境: Generalized Association Plots (GAP 廣義相關圖)。我們以矩陣視覺化來進行統計分析，包含敘述統計、建模、推論，以至於診斷；我們也將統計概念引進矩陣視覺化以處理更複雜之資料形態。GAP可以處理上萬個樣本在上萬個維度(變數)的各式資料矩陣，包含連續、二元、有序、類別、象徵性 (symbolic data)、及與地圖學連結之各類資料。本演講將以深入淺出方式經由各種實例介紹各種主要GAP工作環境。

*須自備筆電且安裝好tensorflow與keras

Abstract: A spectator is invited to shuffle a pack of 52 cards many times and is then asked to secretly pick a number between 1 and 10. The magician displays the cards one at a time and explains that the card in the position of the spectator’s secret number becomes the spectator’s first chosen card. The spectator will use the value of that chosen card as his new number and repeat the process until the magician runs out of cards. Here, aces are worth 1; Jack, Queen, King are worth 5; and all other cards take their face value. We introduce a magic trick that makes the magician can predict the spectator’s last chosen card correctly with high probability about 85%.

*須自備筆電且安裝好tensorflow與keras

Abstract： A main objective of algebraic number theory is to understand the absolute Galois group of the rational field. One way is to study its representations, called Galois representations. Algebro-geometric objects, such as abelian varieties, provide natural Galois representations which have been studied extensively in arithmetic geometry. In this talk, I will discuss Galois representations arising from Jacobian varieties of curves, especially of small genus, and review recent results concerning the size of their image.

*請自備筆電

Abstract： Given a finite group G, any finite-dimensional complex representation is equivalent to a representation of G by matrices with entries from a number field (in fact a cyclotomic field). Thus we may consider reduction of modulo given prime number p of these matrices. Algebra tells us that the number of inequivalent irreducible complex representations of G is the same as the number of conjugacy classes inside G. On the other hand, with prime p fixed, the number of inequivalent mod p irreducible vrepresentations of G is the same as the number of p-regular conjugacy classes of G, i.e. conjugacy classes consisting of elements of order prime to p. When p is prime to |G|, every conjugacy class is p-regular, one has "good" reduction of all the complex representations of G. We are interested in the situation concerning possible "bad" reductions when p divides |G|. Usually given complex representation mod such p will no longer be "semi-simple". It cannot be decomposed into direct sum of irreducible subrepresentations. One has to consider the Jordan-Holder composition series of the mod p representation in question, the mod p invariants are the irreducible representations which come up as "simple" factors of the composition series. I will report on the developments originated from my fall 2016 group representation course, in particular experiences from using the online platform Overleaf collaborating with my students.

Abstract： Face recognition has long been viewed as an important part of the human perception system. The linear discriminant analysis is a renowned feature extraction technique in this field. However, it often suffers from the small sample size problem, since the image dimensionality is usually much higher than the sample size. In this article, we propose a two-step dimension reduction method for obtaining a linear discriminant subspace. Then, discriminant analysis can be carried out in this linear subspace. Our two-step method combines the multilinear principal component analysis (MPCA) in the first step and the partial inverse regression estimate (PIRE) in the second step to resolve the problem of high dimension and small sample size (HDSSS). We also present a strategy for choosing the MPCA rank. In numerical study, the proposed two-step method is shown to outperform the direct PIRE and the competing approaches on benchmark image data sets. Keywords: feature extraction; linear discriminant analysis; multilinear principal component analysis; partial inverse regression estimate. Work done jointly with Y.-H. Sun, S.-Y. Huang, and T.-L. Chen.